Related papers: 2-Dimensional Euclidean Preferences
Aligning robot navigation with human preferences is essential for ensuring comfortable, and predictable robot movement in shared spaces. While preference-based learning methods, such as reinforcement learning from human feedback (RLHF),…
We consider a model where an agent is must choose between alternatives that each provide only an imprecise description of the world (e.g. linguistic expressions). The set of alternatives is closed under logical conjunction and disjunction,…
Two actively researched problem settings in matchings under preferences are popular matchings and the three-dimensional stable matching problem with cyclic preferences. In this paper, we apply the optimality notion of the first topic to the…
A preference system $\mathcal{I}$ is an undirected graph where vertices have preferences over their neighbors, and $\mathcal{I}$ admits a master list if all preferences can be derived from a single ordering over all vertices. We study the…
A homogeneous set of $n$ points in the $d$-dimensional Euclidean space determines at least $\Omega(n^{2d/(d^2+1)} / \log^{c(d)} n)$ distinct distances for a constant $c(d)>0$. In three-space, we slightly improve our general bound and show…
For a set $A$ of $n$ people and a set $B$ of $m$ items, with each person having a preference list that ranks all items from most wanted to least wanted, we consider the problem of matching every person with a unique item. A matching $M$ is…
Social decision schemes (SDSs) map the ordinal preferences of individual voters over multiple alternatives to a probability distribution over the alternatives. In order to study the axiomatic properties of SDSs, we lift preferences over…
We study the problem of designing voting rules that take as input the ordinal preferences of $n$ agents over a set of $m$ alternatives and output a single alternative, aiming to optimize the overall happiness of the agents. The input to the…
In the d dimensional Euclidean space, any set of n+1 independent random points, uniformly distributed in the interior of a unit ball of center O, determines almost surely a circumsphere of center C and of radius R, with n positive and less…
We study the evolution of preferences in multi-population settings that allow matches across distinct populations. Each individual has subjective preferences over potential outcomes, and chooses a best response based on his preferences and…
Consider the voter model on a box of side length $L$ (in the triangular lattice) with boundary votes fixed forever as type 0 or type 1 on two different halves of the boundary. Motivated by analogous questions in percolation, we study…
We investigate binary voting systems with two types of voters and a hierarchy among the members in each type, so that members in one class have more influence or importance than members in the other class. The purpose of this paper is to…
A popular model of preference in the context of recommendation systems is the so-called \emph{ideal point} model. In this model, a user is represented as a vector $\mathbf{u}$ together with a collection of items $\mathbf{x_1}, \ldots,…
We consider a four-player game on the discrete hypercube $Q_n = \{0,1\}^n$, where each of the four players has chosen a single vertex of the hypercube. Such a position is called a profile. Imagine there is a voter at every vertex, and each…
The metric distortion framework posits that n voters and m candidates are jointly embedded in a metric space such that voters rank candidates that are closer to them higher. A voting rule's purpose is to pick a candidate with minimum total…
Polyhedral geometry can be used to quantitatively assess the dependence of rankings on personal preference, and provides a tool for both students and universities to assess US News and World Report rankings.
We investigate (quantifier-free) spatial constraint languages with equality, contact and connectedness predicates as well as Boolean operations on regions, interpreted over low-dimensional Euclidean spaces. We show that the complexity of…
We show that a central linear mapping of a projectively embedded Euclidean $n$-space onto a projectively embedded Euclidean $m$-space is decomposable into a central projection followed by a similarity if, and only if, the least singular…
Preference Inference involves inferring additional user preferences from elicited or observed preferences, based on assumptions regarding the form of the user's preference relation. In this paper we consider a situation in which…
We propose a new version of the spatial model of voting. Platforms of five parties are evolving in a two-dimensional landscape of political issues so as to get maximal numbers of voters. For a Gaussian landscape the evolution leads to a…